Newton and music: From the microcosm to the macrocosm

International Studies in the Philosophy of Science

Volumn 1, Issue 1, 1986, Pages 36-59

  Gouk, Penelope ^a  

^a NONE

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EID: 1542467537     PISSN: 02698595     EISSN: 14699281     Source Type: Journal    
DOI: 10.1080/02698598608573281     Document Type: Article

References (98)

1. 1 An extensive bibliography of this topic is found in S. K. Heninger, Touches of Sweet Harmony: Pythagorean Cosmology and Renaissance Poetics (San Marino, CA, 1974)
2. L. Spitzer, Classical and Christian Ideas of World Harmony: Prolegomena to the Word ‘Stimmung’ (Baltimore, MD, 1963)
3. 2 Notable exceptions to this include A. C. Crombie, ‘Mathematics, Music and Medical Science’, Actes du XIIme congrès international d’histoire des sciences, Paris, 1968 (Paris, 1971), 295-310.
4. S. Drake, ‘Renaissance Music and Experimental Science’, Jl. History of Ideas, 31 (1970), 483-500.
5. The most recent contribution is H. F. Cohen’s excellent study Quantifying Music: the Science of Music at the First Stage of the Scientific Revolution, 1580-1650 (Reidel Publishing Co., Dordrecht, 1984)
6. I am at present completing a book in which the role of music in English natural philosophy is explored more fully, entitled The Anatomy of Music: Sound and Science in Seventeenth-Century England
7. 3 On the relationship between practical and speculative music, see J. C. Kassler, The Science of Music in Britain, 1714-1830: A Catalogue of Writings, Lectures and Inventions, 2 vols (Garland Publishing Inc., New York & London, 1979), 1, xxv-lxii;
8. idem, ‘Music as a Model in Early Science’, History of Science, 20 (1982), 103-139.
9. Newton’s music manuscripts are discussed in S. Jeans, article on Newton in S. Sadie, ed., The New Grove Dictionary of Music and Musicians, 20 vols (London, 1980), xiii, 170-2.
10. The first serious treatment of Newton’s speculative music philosophy is found in J. E. McGuire and P. M. Rattansi, ‘Newton and the “Pipes of Pan”’, Notes and Records of the Royal Society, 21 (1966), 108- 143.
11. Newton’s musical notes are found in Cambridge University Additional MS 4000, fols 104-113, 137-143, CU Add MS 3958(B), fol.31. Extracts from music treatises are found in CU Add MS 3970, fols 1-15. Copies of Newton’s essay ‘On Musick’ are also in Clare College Library, Cambridge, and Christ Church Library, Oxford. On the dating of the early notebooks, see R. Westfall, Never at Rest: A Biography of Isaac Newton (Cambridge University Press, 1980), 83. Westfall does not refer to the music calculations
12. On music education in Cambridge, see N. C. Carpenter, Music in the Medieval and Renaissance Universities (Norman, Oklahoma, 1958), especially 76-8.
13. For a wider discussion of undergraduate education at Cambridge, see J. Gasgoine, ‘The Scientific Revolution and the Universities: the Case of Newton and Restoration Cambridge’, Hist. Sci., 23 (1985), 391-434.
14. J. E. McGuire and M. Tamny, Certain Philosophical Questions: Newton’s Trinity Notebook (Cambridge, 1983), provides a transcription and analysis of CU Add MS 3996.
15. D. T. Whiteside, ‘Isaac Newton: Birth of a Mathematician’, Notes and Records, 19 (1964), 53-62.
16. For a fuller survey of ancient harmonics, see E. A. Lippmann, Musical Thought in Ancient Greece (London, 1964)
17. I. Henderson, ‘Ancient Greek Music’ in E. Wellesz, ed., New Oxford History of Music (Oxford University Press, 1957), i, 336-403;
18. W. Burket, Lore and Science in Ancient Pythagoreanism, trans. E. L. Minar (Cambridge, 1972)
19. For the story of Pythagoras and its earlier sources, see W. H. Stahl, ed., Macrobius’ Commentary on the Dream of Scipio (New York, 1952), especially 3-65, 185-90. See also the references in footnote 1 above
20. On Zarlino and the problem of consonance, see Cohen, Quantifying Music, 1-7.
21. Lippmann, Musical Thought, 45-86 on musical ethics in Greek culture
22. Op. cit., 144-153; Kassler, ‘Music as a Model’, 113.
23. For an introduction to theories of tuning, see J. M. Barbour, Tuning and Temperament (Michigan State College Press, East Lansing, MI, 1953);
24. M. Lindley, ‘Temperaments’ in New Grove, xviii, 660-74; idem, Lutes, Viols and Temperaments (Cambridge University Press, 1984)
25. Lindley, Lutes, 30-2.
26. For a general introduction to the impact of classical texts on Renaissance music theory, see C. V. Palisca, Humanism in Renaissance Musical Thought (Yale University Press, 1985);
27. on acoustics in particular, idem, ‘The Science of Sound and Musical Practice’, in Science and Arts in the Renaissance, ed. J. W. Shirley and F. D. Hoeniger (Associated University Presses, Washington and London, 1985), 59-73.
28. 16 C. V. Palisca, ‘Scientific Empiricism in Musical Thought’, in Seventeenth Century Science and the Arts, ed. H. H. Rhys, (Princeton, 1961), 91-137;
29. D. P. Walker, Studies in Musical Science in the Late Renaissance (E. J. Brill, Leiden and London, 1978), 14-26.
30. Drake, ‘Renaissance Music’ cited above, ref. 2; idem, Galileo Studies: Personality, Tradition and Revolution (Michigan, 1970), 43-62.
31. 18 Palisca, ‘Sound and Musical Practice’, 71.
32. J. Hollander, The Untuning of the Sky: Ideas of Music in English Poetry 1500- 1700 (Princeton, 1961), esp. 61.
33. A similar view is expressed in G. L. Finney, Musical Backgrounds for English Literature: 1580-1650 (Rutgers University Press, New Brunswick, NJ, 1961), 75, 155.
34. 20 P. M. Gouk, ‘Music in Francis Bacon’s Natural Philosophy’ in Francis Bacon: Terminologia e fortuna nel XVII secolo, ed. M. Fattori (Edizioni dell’ Ateneo, Rome, 1984), 139-154.
35. M. Mersenne, Harmonicorum libri (Paris, 1635), lib. 2, prop, xxl, 14-15;
36. G. Galilei, Two New Sciences (1638), trans. S. Drake (Madison, WI, 1974), 96- 108.
37. Cohen, Quantifying Music, 75-114.
38. S. Dostrovsky, ‘Early Vibration Theory: Physics and Music in the Seventeenth Century’, Archive for the History of Exact Sciences, 14 (1974/5), 169-218;
39. F. V. Hunt, Origins in Acoustics: The Science of Sound from Antiquity to the Age of Newton (Yale University Press, New Haven and London, 1978), 109-140;
40. P. M. Gouk, ‘Acoustics in the Early Royal Society 1660-1680’, Notes and Records, 36 (1982), 155-175.
41. W. Brouncker, Renatus Des-Cartes Excellent Compendium of Musick: With Necessary and Judicious Animadversions Thereupon. (London, 1653)
42. See note 14 above; also Cohen, Quantifying Music, 34-45.
43. Op. cit., 45-74.
44. Lindley, Lutes, 32-6.
45. CU Add MS 3958(B) fol 31; CU Add MS 4000, fols 105v, 106. Fuller details of Newton’s calculations may be found in P. M. Gouk, ‘Music in the Natural Philosophy of the Early Royal Society’ (London University Ph.D. thesis, 1982), 250-268.
46. The inventor of the cent system, A. J. Ellis, gives a description of it in his translator’s additions to H. L. F. Helmholtz, On the Sensations of Tone as a Physiological Basis for the Theory of Music (London, 1885), 446-51. For a brief account, see Cohen, Quantifying Music, AA
47. CU Add MS 4000, fol. 108. On different forms of multiple division, see Barbour, Tuning and Temperament, 107-32. Mercator’s treatise is in Oxford, Christ Church MS 1187 D 14, ‘Theoria musices’; see Holder, Treatise, 105-6.
48. Westfall, Never at Rest, 156-75.
49. P.M. Gouk, ‘The Role of Acoustics and Music Theory in the Scientific Work of Robert Hooke’, Annals of Science, 37 (1980), 559-585;
50. J. C. Kassler and D. C. Oldroyd, ‘Robert Hooke’s Trinity College ‘Musick Scripts’, his Music Theory and the Role of Music Theory in his Cosmology’, ibid., 40 (1983), 559-595.
51. Hooke, Micrographia, 15.
52. Gouk, ‘Music in the Early Royal Society’, 33-61;
53. A. E. Shapiro, ‘Kinematic Optics: A Study of the Wave Theory of Light in the Seventeeth Century’, Arch.Hist.Exact Sci., 11 (1973), 134-266.
54. For the section on sound and all its variants, see Isaac Newton’s Philosophiae Naturalis Principia Mathematica. The Third Edition (1726), ed. A. Koyré and I. B. Cohen, 2 vols (Cambridge University Press, 1972), i, 510-34.
55. For a fuller discussion, see Dostrovsky, ‘Early Vibration Theory’, 209-218.
56. From the vast literature on Newton’s optics, I have drawn on the following works by A. E. Shapiro in particular: ‘Newton’s “Achromatic” Dispersion Law: Theoretical Background and Experimental Evidence, Arch.Hist.Exact Sei., 11 (1973), 134-266;
57. ‘The Evolving Structure of Newton’s Theory of White Light and Colour’, Isis, 71 (1980), 211-235;
58. The Optical Papers of Isaac Newton. Vol. 1 Optical Lectures 1670-1672 (Cambridge, 1984)
59. Z. Bechler, ‘Newton’s Search for a Mechanistic Model of Colour Dispersion’, Arch.Hist.Exact Sci., 11 (1973), 1-37.
60. Newton’s letter to the Royal Society and Hooke’s reply are published in The Correspondence of Isaac Newton, ed. H. W. Turnbull et al., 7 vols (Cambridge University Press, 1959-77), i, 92-107, 110-14.
61. A.I. Sabra, Theories of Light from Descartes to Newton (London, 1967), 187-192, 233-4;
62. R. Westfall, ‘Newton’s Reply to Hooke and the Theory of Colours’, Isis, 54 (1963)
63. CU Add MS 3970.3, fols 433-44, 519-28; Z. Bechler, ‘The Disagreeable Case of Newton and Achromatic Reflection’, British Journal for the History of Science, 8 (1975), 101-126.
64. B. J. T. Dobbs, The Foundations of Newton’s Alchemy (Cambridge University Press, 1975), 194-232;
65. idem, ‘Newton’s Alchemy and his Theory of Matter’, Isis, 73 (1982), 511-28.
66. The text of the ‘Hypothesis’ is found in Newton, Correspondence, i, 362-89.
67. Ibid., 376.
68. Shapiro, Newton’s Optical Papers, 542-7.
69. Newton, Correspondence i, 376-7.
70. Shapiro, Newton’s Optical Papers, 544-5.
71. Bechler, ‘Newton’s Search for a Mechanistic Model’, 20-21; Westfall, Never at Rest, 638-49 on the various versions of the Queries and the reintroduction of the universal aether
72. J. E. McGuire, ‘Force, Active Principles, and Newton’s Invisible Realm’, Ambix, 15 (1968), 154-208.
73. CU Add MS 3970, fols 348-9.
74. See, for example, P. Casini, ‘Newton: the Classical Scholia’, Hist.Sci., 22 (1984), 1-58, especially p.8.
75. J. E. McGuire, ‘Neoplatonism and Active Principles: Newton and the Corpus Hermeticum, in R. S. Westman and J. E. McGuire, ed., Hermeticism and the Scientific Revolution (Los Angeles, 1977)
76. J. Jacquot, Thomas Mace, Mustek’s Monument (C.N.R.S., Paris, 1966), ii, 30-36;
77. J. Crossley, ed., The Diary and Correspondence of John Worthington (Chetham Society Publications, Manchester, 1847) i, 27-30.
78. Newton, Correspondence, i, 359-60 (Newton to Oldenburg 30 Nov. 1675)
79. Mace, Mustek’s Monument, 267-70.
80. D. T. Mace, ‘Musical Humanism, the Doctrine of Rhythmus, and the St. Cecilia Odes of Dryden’, Jl. Warburg and Courtauld Insts, 27 (1964);
81. D. P. Walker, ‘Musical Humanism in the 16th and Early 17th Centuries’, Music Review, 2 (1941), 1-13,111-121, 220-227, 288-308; 3 (1942), 55-71. (Repr. in D. P. Walker, Music, Spirit and Language in the Renaissance, ed. P. M. Gouk (Variorum, London, 1985).)
82. CU Add MS 3970, fols 1-11, ‘The Division of a Monochord’; J. Harrison, The Library of Isaac Newton (Cambridge, 1978), 231.
83. On Salmon, see New Grove, xvi, 426-7; Gouk, ‘Music in the Early Royal Society’, 218-31.
84. M. Meibom, Antiquae musicae auctores septem Graece et Latine, 2 vols, Amsterdam, 1652);
85. J. Wallis, Claudii Ptolemaei harmonicorum libri très (Oxford, 1682);
86. idem., ‘Porphyry in harmonia Ptolemaei commentarius’, and ‘Manuelis Bryenni harmonica’, in Opera mathematica, 3 vols (Oxford, 1693- 99), iii, 183-355, 359-508;
87. E. Chilmead, ‘De musica antiqua Graeca’, in J. Fell, ed., Annotationes in Eratosthenem et hymnos Dionysii (Oxford, 1672), 56-69;
88. I. Vossius, De poematum cantu et viribus rhythmi (Oxford, 1672)
89. On Kepler’s music theories, see M. Dickreiter, Der Musiktheoretiker Johannes Kepler (Bern/Munich, 1973);
90. Walker, Musical Science, 34-62.
91. D. Castillejo, The Expanding Force in Newton’s Cosmos (Ediciones de Arte y Bibliofilia, Madrid, 1981)
92. This material found in the Yahuda MSS, Jerusalem, is discussed in R. S. Westfall, ‘Isaac Newton’s Theologiae Gentilis Origines Philosophicae’, in W. Warren Wager, ed., The Secular Mind: Transformations in Faith in Modern Europe (Holmes and Meier, New York, 1982), 15-34.
93. idem, ‘Newton’s Theological Manuscripts’, in Z. Bechler, ed., Contemporary Newton Research, (Reidel, Dordrecht, 1982), 129-143. In his forthcoming publication, ‘Newton’s Comets and the Transformation of Astrology’, Dr Simon Schaffer underlines the significance of the political and ideological context, within which Newton evolved his ideas. I am grateful to Dr Schaffer for letting me read a typescript of his paper and providing information about the manuscripts
94. On the classical scholia, see McGuire and Rattansi, ‘Newton and the “Pipes of Pan”’, and Casini, ‘Newton’s Classical Scholia’. The Yahuda MS 17.3, especially fols 1-2 contains the Pythagorean material of Origines; Royal Society Gregory MS 247, especially fols 11-12 contains the similar material in the draft scholia
95. Walker, Musical Science, 27-33.
96. Newton, Correspondence, iv, 272-3 (Harington to Newton, 22 May 1698). Kassler argues convincingly from internal evidence that the year must be 1698 rather than 1693 as given in the Correspondence: Kassler, Science of Music, ii, 448-50.
97. Newton, Correspondence, iv, 274-6 (Newton to Harington 30 May 1698)
98. That the idea of order and proportion continued to be a fundamental concept in the arts as well as natural philosophy is demonstrated in M. C. Battestin, The Providence of Wit: Aspects of Form in Augustan Literature and the Arts (Oxford University Press, 1974), especially 1-57.